Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices

TL;DR

The work examines how quasiperiodicity in optical lattices and on-site interactions shape Bose-glass and superfluid phases in ultracold bosons, deploying a single-layer Bose-Hubbard model with a quasiperiodic potential and analyzing ground-state and quench dynamics via a site-factorized and time-dependent Gutzwiller approach. It demonstrates that at low filling, increasing the on-site interaction $U$ delocalizes bosons and induces a BG-to-SF transition through percolation of SF regions, while at higher filling a reentrant return to BG occurs due to fragmentation of a percolated SF network. The quench dynamics reveal starkly different responses for intraphase versus interphase quenches, with SF-to-BG quenches causing abrupt connectivity loss and vortex proliferation, and BG-to-SF quenches producing oscillatory percolation and a gradual decrease in $IPR$, signaling the gradual restoration of coherence. These findings illuminate the competition between quasiperiodicity and interactions in engineered optical lattices and have direct relevance for current experiments on twisted bilayer and quasicrystalline lattices.

Abstract

We investigate the ground-state and dynamical properties of ultracold Bose gases in optical lattices with a quasicrystal structure, inspired by recent experiments on twisted bilayer and quasicrystalline optical lattices. The interplay between on-site repulsive interactions and the quasiperiodic potential leads to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose-glass (BG) phase-characterized by disconnected superfluid (SF) regions-into a robust SF phase with a percolated network of SF clusters. This transition is quantitatively identified via the percolation probability. At higher filling factors, we uncover a reentrant behavior: with increasing interaction, the system first changes from BG to SF, but further strengthening reverses the trend, restoring the BG phase. This reentrance originates from an interaction-driven rearrangement of particles, where a percolated SF network fragments into isolated SF islands as repulsion dominates. The quench dynamics show distinct transient features: intraphase quenches cause minor variations in the percolation probability and the inverse participation ratio (IPR), while interphase quenches produce strong responses. In particular, an SF-to-BG quench exhibits an abrupt loss of global SF connectivity, whereas a BG-to-SF quench shows oscillatory percolation and a gradual IPR decrease, stabilizing the SF phase. These results elucidate the competition between quasiperiodicity and interactions in ultracold Bose gases and offer insights relevant to current experiments with twisted bilayer and quasicrystal optical lattices.

Figures (5)

• Figure 1: Phase diagram and representative real-space distributions. (a) Phase diagram for a system of $100$ particles on a $51\times51$ square lattice, where the black solid line is the phase boundary between BG (top) and SF (bottom) phases. Inset: Dependence of the percolation probability $\mathcal{P}$ (blue curve) and the inverse participation ratio (IPR; red curve) on $U/J$ for points along the dashed line indicated in the phase diagram. The inserted SF order-parameter distributions correspond to the nearby red points marked in the main plot. (b) Real-space distributions of the particle density $\left\langle \hat{n}_{i}\right\rangle$, the amplitude of the SF order parameter $|\langle\hat{b}_{i}\rangle|$, and the discrete field $S_{i}$ near the phase boundary ($M_{r}/J=5.9$). See text for more details.
• Figure 2: Phase diagram and representative real-space distributions. (a) Phase diagram for a system of $196$ particles on a $51\times51$ square lattice, where the black solid line is the phase boundary between BG (upper) and SF (lower) phases. Inset: Dependence of the percolation probability $\mathcal{P}$ (blue curve) and IPR (red curve) on $U/J$ for points along the dashed line indicated in the phase diagram. (b) Real-space distributions of the particle density $\left\langle \hat{n}_{i}\right\rangle$, the amplitude of the SF order parameter $|\langle\hat{b}_{i}\rangle|$, and the discrete field $S_{i}$ near the phase boundary ($M_{r}/J=8$). See text for more details.
• Figure 3: (a) Phase diagram of the system at $N=100$ with quench directions marked with arrows. (b) Time dependence of the IPR of the corresponding quench dynamics. (c) Time dependence of the percolation probability $\mathcal{P}$ of the corresponding quench dynamics. Representative real-space distributions of the amplitude of the SF order parameter $|\langle\hat{b}_{i}\rangle|$, the phase $\theta_{i}\equiv\arg\langle\hat{b}_{i}\rangle$ of the SF order parameter, local winding number $w_{i}$ of the phase field $\theta_{i}$, and the discrete field $S_{i}$ during (d) intraphase and (e) interphase quench processes indicated by the arrows in (a). See text for more details.
• Figure 4: Phase diagram and representative real-space distributions. (a) Phase diagram for a system of $1024$ particles on a $51\times51$ square lattice. Inset: Dependence of the percolation probability $\mathcal{P}$ (blue curve) and IPR (red curve) on $U/J$ for points along the dashed line indicated in the phase diagram. (b) Real-space distributions of the particle density distribution $\left\langle \hat{n}_{i}\right\rangle$, the amplitude of the SF order parameter $|\langle\hat{b}_{i}\rangle|$, and the discrete field $S_{i}$ of four points along the dashed line ($M_{r}/J=25$). See text for more details.
• Figure 5: Dependence of the spatially averaged SF order parameter $\sum_{i}|\langle\hat{b}_{i}\rangle|/N_{\mathrm{lat}}$ on the interaction strength at different filling factors. The aperiodic potential strength is fixed at $M_{r}=7$, and the lattice size is $L=51$ ($N_{\mathrm{lat}}=51\times51=2601$).